Nonlinear waves and coherent structures in quasi-neutral plasmas excited by external electromagnetic radiation

Abstract

Starting from the Vlasov-Maxwell equations describing the dynamics of various species in a quasi-neutral plasma, an exact relativistic hydrodynamic closure for a special type of water-bag distributions satisfying the Vlasov equation has been derived. It has been shown that the set of equations for the macroscopic hydrodynamic variables coupled to the wave equations for the self-consistent electromagnetic field is fully equivalent to the Vlasov-Maxwell system.Based on the method of multiple scales, a system comprising a vector nonlinear Schrodinger equation for the transverse envelopes of the self-consistent plasma wakefield, coupled to a scalar nonlinear Schrodinger equation for the electron current velocity envelope, has been derived.Using the method of formal series of Dubois-Violette, a traveling wave solution of the derived set of coupled nonlinear Schrodinger equations in the case of circular wave polarization has been obtained. This solution is represented as a ratio of two formal Volterra series. The terms of these series can be calculated explicitly to every desired order.PACS numbers: 29.20.-c, 52.38.-r, 52.35.-g

Relativistic nonlinear whistler waves in cold magnetized plasmas

“…Omitting details of the calculation procedure, which can be found in Ref. 19, we state here only the final result…”

“…The system of nonlinearly coupled Duffing equations (87) and (88) can be solved by utilizing a nonconventional method known as the method of formal series of Dubois-Violette 15,19 . The basic idea of this technique is to represent the solution of a generic nonlinear equation as a ratio of two formal Volterra series in powers of a (formal) perturbation parameter, rather than a conventional power series provided by standard perturbation theory.…”

“…These waves propagate parallel to the applied magnetic field being circularly polarized in a plane transverse to the direction of propagation. Since their discovery in the end of 19-th century, it has become conventional in the physics of magnetized plasmas to call such structures waves in the whistler mode.…”